DOI: https://doi.org/10.20535/2305-9001.2013.68.33982

### FATIGUE FRACTURE OF THIN PLATES WITH STRESS CONCENTRATORS UNDER UNIAXIAL ASYMMETRICAL LOADING

А в Плащинская

#### Abstract

The problem of fatigue crack growth from a stress concentrator in thin finite plates under high-cyclic uniaxial asymmetrical loading is considered. As the stress concentrators are considered an elliptical hole, circular hole and central crack. Purpose. Testing the model of fatigue fracture based on the joint consideration of boundary-value problem of fracture mechanics and damage kinetics problem of the continuum damage theory on the solution of the problem of the growth of a crack in a thin finite plate with stress concentrators under uniaxial asymmetrical high-cycle loading. Methodology/ approach. It is assumed that fatigue damage accumulation is the cause of crack motion. Two-stage process damage accumulation involves the incubation stage and crack propagation stage. This process is described by scalar parameter of damage ω∈[0;1]. The condition of the damage parameter equality to 1 is taken as the criterion of the fatigue fracture front initiation and movement. It is assumed that main part of body is deformed linear-elastically while all non-linear effects are concentrated in plastic zones at the crack tip. According to presented model the fatigue crack increases step by step on the length of cyclic plastic zone. The lengths of plastic zones near crack tip are defined on base modified Dugdale model. Findings The numerical analytical solution is obtained on basis of fatigue crack growth two-stage theoretical model and equivalent stresses criterion reduced asymmetrical loading to equivalent symmetrical cyclic loading on rupture time. The calculation results using model agree well with those obtained by experiment.

#### Keywords

fatigue crack; asymmetrical loading cycle; thin finite plates; elliptical hole; circular hole; crack; uniaxial tensioncompression; damage; plastic zone.

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#### References

Grover, H.J., Hyler W.S., Kuhn P., Landers C.B. and Howell F.M., Axial-Load Fatigue Properties of 24S-T and 75S-T Aluminum Alloy as Determined in Several Laboratories. NACA TN-2928, 1953, 64 р.

Hudson C.M., Effect of stress ratio on fatigue-crack growth in 7075-T6 and 2024-T3 aluminum-alloy specimens. NASA TN D-5390, 1969, pp. 34.

Golub V.P., Plashchynska A.V., Phenomenological model of fatigue crack growth in perfectly plastic infinite plates under completely reversed uni-axial loading. International applied mechanics Volume 41, no 12, 1426-1436.

Plashchynska A.V., Kinetika rosta ustalostnyh treshchin v tonkih plastinah konechnyh razmerov pri assimmetrichnom nagruzhenii [Kinetics of fatigue cracks growth in thin finite plates at asymmetric loading] Journal of Mechanical. Engineering of the National Technical University of Ukraine “Kyiv Polytechnic Institute”, 2010, no 58, pp. 189-194.

Golub V.P., Krizhanovskii V.I., Pogrebnyak A.D., Kochetkova Y. S. Fatigue strength of metallic and composite materials in the asymmetric tension and compression. Prikladnaya Mekhanika, 2006. Vol. 42 (52), no 1, pp. 48-58.

Newman, J. C., Jr. FASTRAN-II – A fatigue crack growth structural analysis program, NASA-TM-104159, 1992, 103 р.

Savruk, М.P. Koeffitsyentu intensivnosti napriageniy v telah s treshchinami [The stress intensity factors in the bodies with cracks] Fracture mechanics and strength of materials. Vol. 2. Kiev: Naukova dumka., 1988, 618 p.

Illg, W. McEvily A.J.,Jr. The rate of fatigue-crack propagation for two aluminum alloys, NACA TN 4394, 1958, 47 p.

#### GOST Style Citations

1. Grover, H.J. Axial-Load Fatigue Properties of 24S-T and 75S-T Aluminum Alloy as Determined in Several Laboratories / Grover H.J., Hyler W.S., Kuhn P., Landers C.B. and Howell F.M. H // NACA TN-2928, 1953. – 64 р.

2. Hudson C.M. Effect of stress ratio on fatigue-crack growth in 7075-T6 and 2024-T3 aluminum-alloy specimens // NASA TN D-5390, 1969, pp.34.

3. Golub V.P Phenomenological model of fatigue crack growth in perfectly plastic infinite plates under completely reversed uni-axial loading./ V.P. Golub, A.V. Plashchynska // International applied mechanics Volume 41,number 12, 1426-1436

4. Плащинская, А.В Кинетика роста усталостных трещин в тонких пластинах конечных размеров при асимметричном нагружении //Вісник НТУУ КПІ Машинобудування. – 2010. – С. 189-194.

5. Голуб В.П. Усталостная прочность металлических и композитных материалов при асимметричном растяжении- сжатии/ В.П. Голуб, В.И. Крижановский, А.Д. Погребняк, Е.С Кочеткова. // Прикл. механика.- 2006.- Том 42 (52), №1.- С. 48-58.

6. Newman, J. C., Jr. FASTRAN-II – A fatigue crack growth structural analysis program// NASA-TM-104159, 1992. – 103 р.

7. Саврук, М.П. Коэффициенты интенсивности напряжений в телах с трещинами // Механика разрушения и прочность материалов. – Т. 2 //Киев: Наукова думка. – 1988. – 618 с.

8. Illg, W. The rate of fatigue-crack propagation for two aluminum alloys / W.Illg, A.J.,Jr.McEvily // NACA TN 4394, 1958. – 47 p.

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